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Using ruler and compasses only, draw a parallelogram whose diagonals are 4 cm and 6 cm long and contain an angle of 75°. Measure and write down the length of one of the shorter sides of the parallelogram.

Rectilinear Figures

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Answer

Steps of construction:

Let AC = 4 cm and BD = 6 cm.

  1. Draw AO = 12AC=12×4=2 cm and\dfrac{1}{2}AC = \dfrac{1}{2} \times 4 = 2\text{ cm and} produce AO to C such that OC = OA.
  2. At O construct ∠COP = 75°.
  3. From OP cut off OD = 12BD=12×6=3\dfrac{1}{2} BD = \dfrac{1}{2} \times 6 = 3 cm, produce DO to B such that OB = OD.
  4. Join AB, BC, CD and DA. Then ABCD is the required parallelogram.
Using ruler and compasses only, draw a parallelogram whose diagonals are 4 cm and 6 cm long and contain an angle of 75°. Measure and write down the length of one of the shorter sides of the parallelogram. Rectilinear Figures, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

On measuring shorter sides, we get

AB = CD = 3.1 cm.

Hence, length of shorter side = 3.1 cm.

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